Constrained Quantization for Uniform Distributions with Two Constraint Families

2023/09/20 by Singh, Pavjeet, Katiyar, S. K., Pandey, Megha +1
Computer Science · #60E05 #94A34 #Advanced Data Compression Techniques #FOS: Mathematics #Image and Signal Denoising Methods #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2309.11498

openalex publication_date 2023/09/20 · openalex created_date 2023/09/23 · openalex updated_date 2026/07/28

Abstract

In this paper, we first consider a family of constraints given by straight lines. For a uniform probability distribution, we determine the constrained optimal sets of n-points and the corresponding nth constrained quantization errors for all positive integers n. In addition, we calculate the constrained quantization dimension and the constrained quantization coefficient with respect to this family of constraints. Next, we turn to another family of constraints, consisting of concentric circles. For the same probability distribution, we present a methodology to compute the constrained optimal sets of n-points and the corresponding nth constrained quantization errors for all positive integers n. Finally, we conclude the paper with a summary of the results and a discussion of future research directions.

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